Density of the lexicographically ordered space $\{0,1\}^ \alpha$
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- by W. W. Comfort PDF
- Proc. Amer. Math. Soc. 109 (1990), 523-525 Request permission
Abstract:
For an infinite cardinal $\alpha$, the lexicographically ordered space ${\left \{ {0,1} \right \}^\alpha }$ is denoted $\Lambda (\alpha )$; its density is denoted $d\Lambda (\alpha )$. Completing a computation left unfinished elsewhere, we prove $d\Lambda (\alpha ) = {2^{_\smile ^\alpha }}$.References
- W. W. Comfort and S. Negrepontis, The theory of ultrafilters, Die Grundlehren der mathematischen Wissenschaften, Band 211, Springer-Verlag, New York-Heidelberg, 1974. MR 0396267, DOI 10.1007/978-3-642-65780-1 W. W. Comfort and D. Remus, Long chains of Hausdorff topological group topologies,(submitted for publication). M. A. Maurice, Compact ordered spaces, Mathematical Centre Tracts, no. 6, Mathematisch Centrum, Amsterdam, 1964.
- Wacław Sierpiński, Sur une propriété des ensembles ordonnés, Fund. Math. 36 (1949), 56–67 (French). MR 31528, DOI 10.4064/fm-36-1-56-67
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 523-525
- MSC: Primary 54A25; Secondary 54F05
- DOI: https://doi.org/10.1090/S0002-9939-1990-1000150-9
- MathSciNet review: 1000150